the Creative Commons Attribution 4.0 License.

the Creative Commons Attribution 4.0 License.

# Evaluation of UV aerosol retrievals from an ozone lidar

### Bo Wang

### Michael J. Newchurch

### Kevin Knupp

### Paula Tucker

### Edwin W. Eloranta

### Joseph P. Garcia

### Ilya Razenkov

### John T. Sullivan

### Timothy A. Berkoff

### Guillaume Gronoff

### Liqiao Lei

### Christoph J. Senff

### Andrew O. Langford

### Thierry Leblanc

### Vijay Natraj

Aerosol retrieval using ozone lidars in the ultraviolet spectral region is challenging but necessary for correcting aerosol interference in ozone retrieval and for studying the ozone–aerosol correlations. This study describes the aerosol retrieval algorithm for a tropospheric ozone lidar, quantifies the retrieval error budget, and intercompares the aerosol retrieval products at 299 nm with those at 532 nm from a high spectral resolution lidar (HSRL) and with those at 340 nm from an AErosol RObotic NETwork radiometer. After the cloud-contaminated data are filtered out, the aerosol backscatter or extinction coefficients at 30 m and 10 min resolutions retrieved by the ozone lidar are highly correlated with the HSRL products, with a coefficient of 0.95 suggesting that the ozone lidar can reliably measure aerosol structures with high spatiotemporal resolution when the signal-to-noise ratio is sufficient. The actual uncertainties of the aerosol retrieval from the ozone lidar generally agree with our theoretical analysis. The backscatter color ratio (backscatter-related exponent of wavelength dependence) linking the coincident data measured by the two instruments at 299 and 532 nm is 1.34±0.11, while the Ångström (extinction-related) exponent is 1.49±0.16 for a mixture of urban and fire smoke aerosols within the troposphere above Huntsville, AL, USA.

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A tropospheric ozone differential absorption lidar (DIAL) makes measurements of vertical ozone profiles, typically at two wavelengths chosen between 277 and 300 nm with a separation less than 12 nm, by weighing several parameters such as the ozone absorption cross sections, solar background, dynamic range of the detection system, and interference from aerosols and other species (e.g., Alvarez et al., 2011; Browell et al., 1985; De Young et al., 2017; Fukuchi et al., 2001; Kempfer et al., 1994; McDermid et al., 2002; Proffitt and Langford, 1997; Strawbridge et al., 2018; Sullivan et al., 2014). Vertical aerosol profiles are of high interest not only because they are needed for aerosol correction in ozone lidar retrievals (Steinbrecht and Carswell, 1995) but also because simultaneous ozone and aerosol vertical profile measurements provide unique information on their interactions and on sources of pollutant transport (Browell et al., 1994; Langford et al., 2020; Newell et al., 1999). However, there is currently no consensus on the reliability of the aerosol retrievals produced by ozone lidars due to the difficulty of solving the three-component lidar equation and the large variability in aerosol optical properties associated with the multiplicity of aerosol types and size distributions.

The most widely used solution for the elastic single-wavelength aerosol
lidar equation is the analytic method developed by Klett (1981). The
inversion method then inspired Fernald (1984) to publish a computer
algorithm scheme to solve the more general two-component (aerosol and
molecular) atmospheric lidar equation. The Klett (1981) inversion requires
a priori value for the lidar ratio (i.e., aerosol extinction-to-backscatter ratio,
represented by “*S*” hereafter) to link the aerosol backscatter with its
extinction for solving the lidar equation. Lasers used for aerosol lidars
are preferred in the visible and infrared bands, typically 532 and 1064 nm for an Nd:YAG laser or 694 nm for ruby laser (Russell et al., 1979), where the
ozone absorption is much smaller than molecular and Mie scattering. In the
ultraviolet (UV) band for an ozone lidar, the ozone absorption may not be
trivial. Some ozone lidars have an aerosol channel available, either
independently or sharing receiving optics with the ozone channel (e.g.,
Browell et al., 1994; De Young et al., 2017; Gronoff et al., 2019; Kovalev
and McElroy, 1994; Uchino and Tabata, 1991). For most of the traditional
two-wavelength ozone lidars without an aerosol channel, although there has
been some discussion about the aerosol retrieval algorithm (e.g., Eisele and
Trickl, 2005; Langford et al., 2019; Papayannis et al., 1999; Sullivan et
al., 2014), the evaluation of the aerosol retrieval product and its error
budget have rarely been addressed. Due to a significant wavelength difference
with aerosol lidars, several aspects of the aerosol retrieval using an ozone
lidar are worth noting. First, the signal-to-noise ratio (SNR) for ozone
lidars decays quicker with altitude due to more significant UV molecular
(i.e., Rayleigh) scattering and ozone absorption resulting in a lower
retrievable altitude than aerosol lidars. Second, since the molecular and
ozone components become more important at UV wavelengths compared to visible
and infrared wavelengths, the uncertainties in aerosol retrieval propagated
from the calculation of these two components are expected to be larger for
ozone lidars than for aerosol lidars. Third, *S* and the wavelength dependence
used for the ozone lidar wavelengths may be different from those used for
the longer aerosol lidar wavelengths (Ackermann 1998; Eck et al., 1999).

The primary objectives of this article are to investigate the performance of our aerosol retrieval algorithm and to quantify its error budget for the ozone lidar. The secondary goal is to seek the overall wavelength dependence between the aerosol optical properties measured by the ozone lidar at 299 nm and by a high spectral resolution lidar (HSRL) at 532 nm.

## 2.1 Ozone lidar

The Rocket-city Ozone (O_{3}) Quality Evaluation in the Troposphere
(RO_{3}QET) lidar is located on the campus of The University of Alabama in Huntsville (UAH) at 34.725^{∘} N, 86.645^{∘} W at 206 m a.s.l. and is one of the six systems of the Tropospheric Ozone Lidar Network (TOLNet) (http://www-air.larc.nasa.gov/missions/TOLNet, last access: 20 September 2020). This system
measures ozone from 0.1 km up to about 12 km during nighttime and up to
about 6 km during daytime with a temporal resolution of 2 min. The vertical
resolution of the lidar retrievals varies from 150 m in the lower
troposphere to 750 m in the upper troposphere in order to keep the
measurement uncertainty within ±10 % (Kuang et al., 2013).

The transmitter comprises two Raman-shifted lasers at 289 and 299 nm. Two 30 Hz, 266 nm Nd:YAG lasers pump two 1.8 m Raman cells with mixtures of active gas and buffer gas to generate 289 and 299 nm lasers with an average pulse energy of about 5 mJ. The receiving system consists of three receivers with diameters of 2.5, 10, and 40 cm and four photomultiplier tubes (PMTs) similar to that described by Kuang et al. (2013) except that the solar filters have been replaced by 300 nm short-pass filters for all telescopes. Channels 1, 2, 3, and 4 represent the 2.5 cm, 10 % of the 10 cm, 90% of the 10 cm, and the 40 cm telescope channels, respectively. Since the modification of channel 4 through the addition of narrowband solar filters was not completed before the time period of this study, data from this channel were not used in this work, with the net result that uncertainties for ozone retrievals above 6 km during daytime were often too large due to the strong solar background. Lidar-signal counting was accomplished by four Licel transient recorders (Licel company, Germany) with both analog and photon-counting (PC) modes, with a sampling rate of 40 MHz corresponding to a 3.75 m fundamental resolution. The cloud base height is determined by the following empirical method. Derivatives of the logarithm of the offline analog signal are calculated for a lidar-signal profile, and the first range bin at which the derivative is greater than a certain threshold is considered to be the cloud base height. The threshold is chosen empirically based on the lidar SNR and the vertical resolution. Therefore, lidar data with cloud base lower than 2 km were discarded. The cloud filtering process should be conducted carefully, because an elastic lidar without a polarization channel is not capable of accurately distinguishing aerosols and clouds solely through their backscatter properties. Five 2 min lidar data intervals were combined to give a 10 min lidar-signal integration time to improve the SNR. Further, six of the 3.75 m fundamental bins were integrated for all channels. In addition, dead-time correction (for PC signal only), background correction, analog and PC signal merging, and signal-induced noise correction were performed.

## 2.2 Aerosol retrieval and uncertainty estimation

The aerosol profiles were retrieved with an iterative DIAL algorithm (Kuang
et al., 2011). A brief description of this algorithm is provided in this
section, with further details in Appendix A. A first-order Savitzky–Golay
differentiation filter with a second-degree polynomial was applied to the
logarithm of the signal ratios to compute the first-cut ozone profile. This
initial ozone profile was substituted back into the three-component lidar
equation to derive the profile of aerosol backscatter coefficients at 299 nm by assuming a constant *S* of 60 sr and boundary value of the aerosol
backscatter coefficient at a far-range reference altitude (about 10 km).
During the daytime, the ozone retrieval was limited by the lower SNR of the
289 nm channel, but the 299 nm channel had much better SNR due to lower
atmospheric extinction, and it was able to measure aerosol up to higher
altitudes. *S* has high variability as a function of aerosol characteristics,
humidity, and wavelength (Ackermann, 1998; Strawbridge et al., 2018;
Mishchenko et al., 1997). The *S* a priori value assumed for this study represents a
mix of urban and smoke aerosols during the lidar observations (Ackermann,
1998; Burton et al., 2012; Cattrall et al., 2005; Groß et al., 2013;
Müller et al., 2007). The a priori value is application dependent. In the aerosol
retrieval uncertainty discussion in Appendix B, we assume a ±20 %
uncertainty for *S* based on an average standard deviation obtained from prior
observations (Müller et al., 2007).

Molecular backscatter and extinction profiles were computed from local radiosonde data. Then, the aerosol profile was substituted into the lidar equation again to obtain a stable solution, usually within three iterations. This aerosol profile was further employed to calculate the aerosol correction for ozone retrievals using the first-order Taylor approximation (Browell et al., 1985) by assuming a power-law wavelength dependence for the aerosol extinction and choosing an appropriate Ångström exponent. Since this work focuses only on aerosol retrieval, details of the ozone correction will be described in a future article. Finally, the aerosol profiles derived by the three altitude channels were merged into a single profile in the overlapping altitude zones, i.e., 0.5–1 km for channels 1 and 2 and 1.5–2 km for channels 2 and 3.

The primary uncertainty sources for the aerosol lidar retrievals are the
uncertainties in lidar-signal measurement, boundary value assumption for
aerosol backscatter coefficient, air density measurement, *S* a priori value, and ozone
profile input. The relative importance of these sources is altitude
dependent. In the planetary boundary layer (PBL) where the air is typically
turbid, the *S* uncertainty is dominant, while other sources are minor (only a few
percent). The uncertainty of *S* influences the uncertainty of the aerosol
backscatter through a complicated relationship. However, the magnitude of
the above two uncertainties can be approximately seen to be close. At the
far range (higher than 7 km), the lidar-signal detection noise and inaccurate
boundary value assumption are important. Influence from both of the above
sources, especially the boundary value, on the aerosol retrieval quickly
decreases towards the ground from the far range. In the middle range (PBL
top to 7 km), both the air density measurement error and lidar-signal
detection noise are essential. Uncertainty due to ozone profile input is
relatively unimportant and is only a few percent at most altitudes. Figure B1
presents an example of the aerosol backscatter uncertainty calculated from
10 min nighttime RO_{3}QET lidar data. The error budget estimate generally
justifies the choice of using 6 km as the maximum altitude for the
RO_{3}QET and HSRL comparison since the total uncertainty for the RO_{3}QET
aerosol retrieval could be unacceptably large (i.e., persistently larger
than 100 %).

## 2.3 HSRL

The University of Wisconsin HSRL (Eloranta, 2005) was deployed in
Huntsville, AL, from 19 June to 4 November 2013 and operated almost 24 h
every day to support the Studies of Emissions and Atmospheric Composition,
Clouds and Climate Coupling by Regional Surveys SEAC^{4}RS campaign (Kuang
et al., 2017). The HSRL transmitter was a diode-pumped Nd:YAG laser at 532 nm with a pulse energy of about 50 µJ and a pulse repetition frequency
of 4 kHz. The expanded laser beam was transmitted coaxially with a 40 cm telescope with a tiny field of view (FOV) of 100 µrad to reduce solar
background. The HSRL spectral filtering can separate the molecular
backscatter from the aerosol backscatter due to the molecular Doppler
broadening effect, while the particulate backscatter remains spectrally
unbroadened. Aerosol backscatter coefficients can then be calculated as the
difference between the total return and the molecular component (Grund and
Eloranta, 1991). In principle, aerosol extinction can be computed by
comparing the measured attenuated molecular backscatter to a reference,
unattenuated molecular backscatter profile that is calculated from the
radiosonde-measured air density profile, or a numerical model (Hair et al.,
2008). However, small and fast signal fluctuations were found in the partial
overlap region (between the surface and about 4.5 km) for the data taken in
Huntsville, so aerosol extinction below 4.5 km cannot be derived with
satisfactory precision. The signal fluctuations were probably caused by small
optical misalignments from temperature changes within the lidar system (Reid
et al., 2017). The aerosol backscatter calculation is not affected by the
lidar-signal fluctuations since any range-dependent instrument effects are
canceled out. Therefore, we focus on the aerosol backscatter intercomparison
between the HSRL and RO_{3}QET. If aerosol extinction is needed for the
HSRL, we will calculate it from the aerosol backscatter by assuming a
constant lidar ratio. The HSRL provides aerosol products with a 30 m vertical resolution and 1 min temporal resolution from near the surface to
15 km. To achieve sufficient SNR for both HSRL and ozone lidar and to reduce
the uncertainty arising from the clock bias of the controlling computers, we
adopt 10 min temporal average and 30 m vertical average for both HSRL and
ozone lidar in the intercomparison study. The HSRL has a backscatter
measurement precision better than 10^{−7} m^{−1} sr^{−1} for a
1 min signal average (Reid et al., 2017), which represents an estimated
precision for the extinction coefficient of better than $\mathrm{2}\times {\mathrm{10}}^{-\mathrm{6}}$ m^{−1} for a 10 min average.

We select four time periods (21–23 June, 14–15 August, 27–28 August, and 5–6 September 2013) to investigate the ozone lidar capability for measuring aerosol column and range-resolved profiles. All four cases have coincident ozone lidar and HSRL observation periods longer than 24 h, which is fully covering the convective mixing layer development and collapse processes (Klein et al., 2019) and having significant smoke layers in the free troposphere. Due to the significant extinction and potential multiple scattering caused by clouds, the ozone lidar is incapable of measuring either ozone or aerosol accurately above clouds, especially thick clouds. Therefore, data contaminated by clouds is filtered out. At this time, the narrowband interference filters had not been incorporated into the receiving system, and the wideband filter resulted in substantial solar background during the daytime; hence, we set 6 km a.s.l. as the maximum altitude for intercomparison. The uncertainty of the aerosol retrieval owing to lidar-signal measurement error is dominant at far range and is determined by the lidar SNR, as shown in Appendix B2. The solar background is an important noise resulting in the lidar-signal measurement error during daytime and is partly responsible for the high aerosol retrieval uncertainty above 6 km as shown by the example in Fig. B1. The 10 min HSRL profiles are interpolated to the times of the ozone lidar data.

First, we investigate the correlation of the integrated (or column) aerosol
backscatter between the ozone lidar and HSRL to obtain a general
relationship between their averages. Figure 1 shows that the RO_{3}QET-
and HSRL-derived integrated backscatter coefficients for all four cases are
highly correlated, with a Pearson correlation coefficient of 0.99. The root-mean-square error (RMSE), the standard deviation of the residuals, is
negligibly small at $\mathrm{1}\times {\mathrm{10}}^{-\mathrm{3}}$ sr^{−1}, suggesting that the linear
regression equation can accurately represent the relationship between the
aerosol optical depth (AOD) measured by the two instruments. The 493 sampling profiles cover 82 h of coincident ozone lidar and HSRL observations. We define the aerosol
backscatter color ratio (*å*_{β}) as (Burton et al., 2012):

where ${\mathit{\beta}}_{\mathrm{A}}^{\mathrm{299}}$ and ${\mathit{\beta}}_{\mathrm{A}}^{\mathrm{532}}$ represent the aerosol
backscatter coefficient at 299 and 532 nm, respectively. The subscript
“*A*” represents the “aerosol” component, which is distinguished from the
“molecular” contribution that is represented by subscript “*M*” in
Appendix B. *å*_{β} is an exponent denoting backscatter-related
wavelength dependence, which is distinguished from the commonly used
Ångström exponent (Ångström, 1929) that refers to the
wavelength dependence of optical thickness or extinction coefficient.
*å*_{β} is also different from another often-used concept, “color
ratio of the lidar ratios”, which refers to the ratio of *S* at two different
wavelengths. The slope of the regression, equal to 2.16, results in the best
least-squares fit value of 1.34 for *å*_{β} at 299 and 532 nm. The
uncertainty of the column ${\mathit{\beta}}_{\mathrm{A}}^{\mathrm{299}}$ is expected to be smaller than
the uncertainty for ${\mathit{\beta}}_{\mathrm{A}}^{\mathrm{299}}$ at a particular altitude and for a
10 min integration time (in Fig. B1) since the average over longer time
and altitude range greatly reduces the random noise as suggested by the
small RMSE in Fig. 1. If the uncertainty of the column ${\mathit{\beta}}_{\mathrm{A}}^{\mathrm{299}}$
measurements is estimated to be 20 %, which is primarily due to the
uncertainty of the *S* a priori value (a systematic error), we can estimate the corresponding
uncertainty for *å*_{β}=1.34 to be ±0.11 by error
propagation from Eq. (1). *å*_{β} has important applications in
aerosol type classification from (spectral) aerosol lidar measurements
(e.g., Cattrall et al., 2005; Hair et al., 2008; Müller et al., 2007).
There is significant variation in *å*_{β} for 532–1064 nm reported
in different studies, with numbers ranging from negative values to 2.3
(Burton et al., 2012; Cattrall et al., 2005; Müller et al., 2007).
However, all of these studies show a larger value of *å*_{β} for
smoke and urban aerosols than for maritime and dust aerosols. Since most
previous studies report *å*_{β} for wavelengths longer than 355 nm,
*å*_{β} calculated in this study for 299–532 nm could provide
valuable data for UV wavelengths.

In practice, aerosol extinction is a more meaningful parameter and more
relevant for several applications than backscatter. For the HSRL, the
extinction coefficients are linearly converted from the backscatter
coefficients by assuming a constant *S*=55 sr with 20 % uncertainty, as in
the same manner as Reid et al. (2017). The estimated Ångström
exponent for 299 and 532 nm is 1.49±0.16, using the data in Fig. 1
after considering uncertainties in *S* for both lidars. The calculated
Ångström exponent is different from the backscatter-related
wavelength exponent because of the wavelength dependence of *S*. The
Ångström exponent from this study (1.49±0.16) is within a
reasonable range compared to previous studies. For example, the
Ångström exponent was measured by a Raman lidar to be between
1.35±0.2 and 1.56±0.2 at 355 nm for smoke aerosols in Canada
(Strawbridge et al., 2018). The Ångström exponent for urban aerosols
was measured to be 1.4±0.5 in Europe and 1.7±0.5 in North
America for 355 and 532 nm (Müller et al., 2007).

The AErosol RObotic NETwork (AERONET) (Holben et al., 1998) provides aerosol
optical depth (AOD) measurements in eight spectral bands between 340 and
1020 nm with a temporal resolution of about 15 min. The measurement
uncertainty for AERONET AOD is within 0.02 and is expected to be larger in
the UV bands (Eck et al., 1999; Holben et al., 2001). Even though the
measurement is at a different wavelength, the AERONET AOD at 340 nm can
provide an additional constraint for the choice of *S* for the RO_{3}QET
aerosol retrieval, especially since both instruments are at the same
location. Figure 2 presents the intercomparison of the RO_{3}QET lidar-derived AOD at 299 nm and all available AOD data at 340 nm (Smirnov et al.,
2000) from the colocated AERONET sun–sky radiometer (data for 21–23 June
are unavailable). The near-surface region is assumed to be homogeneous and
assigned the same aerosol extinction values as the lowest available 30 m layer from the RO_{3}QET retrievals. Then, the aerosol extinction
coefficients are integrated from 0 to 6 km a.s.l. to calculate the
lidar-derived AOD. The omission of aerosol extinction above 6 km and the
homogeneity assumption for the near-surface region are sources of bias for
the comparison since the AERONET instrument measures the total column AOD.
The lidar has more data and higher temporal resolution; therefore, the
lidar-derived AOD is interpolated to the AERONET measurement times. Figure 2
shows that the AOD retrieved by the two instruments has a correlation
coefficient of 0.97 and a small RMSE for a total duration of about 31 h.
The mean percentage difference between the RO_{3}QET and AERONET AOD is
15 *%*±9 %. The *S* a priori value directly affects the AOD calculation. The
lidar-derived AOD is on average 15 % larger than the AERONET AOD due to
the shorter wavelength of the lidar measurement, suggesting that the choice
of *S*=60 sr is appropriate. For a rough estimation, the 1*σ* standard
deviation (9 %) of the differences can be considered the uncertainty of *S* if the variability of these differences are mostly due to the variation in
*S*. Considering that AERONET measures the column-average AOD (with longer
temporal integration), has its own uncertainty, and covers only 38 % of the
total observational period, our assumption for $S=\mathrm{60}\phantom{\rule{0.125em}{0ex}}\mathit{\%}\phantom{\rule{0.125em}{0ex}}\mathrm{sr}\pm \mathrm{20}$ % sr is
appropriate for RO_{3}QET lidar profiling measurements with higher
temporal and vertical resolution and should be good enough to cover various
uncertainty sources. The colocated AERONET data enhance the credibility of
our lidar aerosol retrieval and help evaluate the *S* a priori value, with the caveat that
the 124 paired data covering 31 h are not a large sample set. We do not show
the HSRL–AERONET comparison here since Reid et al. (2017) have done so using
more extensive data in a visible band taken at the UAH site in summer 2013.

Figure 3 presents the intercomparison of the aerosol backscatter retrieved
by the HSRL and the RO_{3}QET lidar for the four cases in 2013. The
HSRL-derived aerosol backscatter coefficients are scaled to 299 nm (represented by “HSRL-converted” hereafter) using the best-fit exponent
value *å*_{β}=1.34. Some clouds lower than 2 km show up in the
HSRL curtains but not in the RO_{3}QET curtains (e.g., 1500–2100 on 15 August and 1500–2100 on 28 August). These low-cloud-contaminated data were
discarded in the RO_{3}QET lidar preprocessing program since the ozone
lidar probes the atmosphere with a shorter wavelength than the HSRL and is,
therefore, more affected by cloud interference. Profiles with clouds higher
than 2 km measured by RO_{3}QET were retained, and the aerosol
retrievals below the clouds were used for the range-resolving
intercomparisons.

In terms of the aerosol measurement evaluation, we pay attention to the two
capabilities of the RO_{3}QET lidar: measuring the PBL diurnal evolution
and measuring free-tropospheric smoke layers. In Fig. 3, the PBL heights
measured by the two lidars, which are identified by large aerosol gradients,
are highly consistent for all cases. The development of the convective
mixing layer in the early morning, an important process responsible for
surface ozone increase, can be visually identified in most RO_{3}QET
curtains (e.g., 14:00–17:00 UTC or 09:00–12:00 LT (local time) in Fig. 3h). The
aerosol structures and evolution in the free troposphere measured by the
RO_{3}QET lidar are highly similar to those measured by the HSRL. For
example, the RO_{3}QET lidar captured an extremely thin aerosol layer at
∼5 km altitude on 27–28 August (Fig. 3g), which probably
originated from the Pacific Northwest fire and has been discussed by Reid et
al. (2017). The large aerosol uncertainties for the RO_{3}QET lidar at far
ranges are consistent with expectation. As demonstrated in Appendix B,
aerosol retrieval uncertainties due to lidar-signal measurement error and
the boundary value chosen at the reference altitude, which are two of the most
important sources of uncertainty, increase with altitude and may exceed
100 % at ∼7 km .

To evaluate the range-resolving capability of the ozone lidar for aerosol
retrieval, we intercompared the aerosol backscatter coefficients, for all
cases, from the two instruments with a 10 min temporal resolution and a 30 m vertical resolution after filtering out cloud-contaminated data, as shown in
Fig. 4. The high correlation coefficient of 0.95 suggests that the
RO_{3}QET lidar can capture the aerosol variability with high
spatiotemporal resolution. The correlation coefficient (0.95) between the
two high vertical resolution retrievals is slightly lower than that between
the RO_{3}QET and column-averaged HSRL retrievals (0.99; see Fig. 1) due
to less vertical averaging. The HSRL-converted backscatter is calculated using
*å*_{β}=1.34 and the regression equation in Fig. 1. We expect
the slope of the data in Fig. 4 to be very close to 1. However, the actual
slope is 1.08, reflecting the fact that there are a large fraction of points
with small aerosol backscatter and larger residuals in clean air (low
aerosol) regions. This is not surprising since the HSRL has higher
measurement precision than the RO_{3}QET lidar so that their relative
differences in clean air regions can be large.

Figure 5 presents the mean and 1*σ* standard deviations of the
relative differences between RO_{3}QET and HSRL retrievals,
(RO_{3}QET-HSRL)/HSRL, to be compared with the theoretical 1*σ*
error calculated as outlined in Appendix B. The HSRL measurements are
considered the “true” values to be compared with the RO_{3}QET
measurements. Both the theoretical and actual 1*σ* values generally
increase with altitude. The actual differences between RO_{3}QET and HSRL measurements are mostly within or of comparable order of magnitude to the theoretical calculation of the RO_{3}QET measurement uncertainties. The
structures of the theoretical uncertainties are consistent with the actual
differences at most altitudes, with few exceptions. For example, the large
discrepancies (red lines compared to blue lines in Fig. 5) occurring at
∼4.5 km in Fig. 5c and ∼1.5 km in Fig. 5d are primarily because of small-number division effects for the
extremely clean atmospheric layers (also see Fig. 3). Aerosol backscatter
of clean air can be accurately measured by the HSRL, but it may be beyond the
measurement sensitivity of RO_{3}QET.

In Fig. 5, the RO_{3}QET-measured aerosols are generally higher than the
HSRL-measured aerosols between 5 and 6 km, so the RO_{3}QET-HSRL
differences are biased to positive altitude values. These positive biases
can be due to two reasons. First, the RO_{3}QET-derived aerosol
extinction above 5 km is obviously larger than that from HSRL during daytime
due to the solar background impact, which is especially strong in the
summer. The relative differences are even worse in clean (compared to
turbid) regions during the daytime because of the small-number division
effect mentioned earlier. It can be seen from Fig. 3 that RO_{3}QET
nighttime retrievals above 5 km and daytime retrievals below 5 km are
relatively good due to either lower solar background or larger lidar signal
resulting in better SNR. There were both clean and smoky layers between 5
and 6 km for the four cases; therefore, the positive differences cannot be
explained solely by the lower capability of RO_{3}QET for measuring clean
air. We hypothesize that another reason causing the positive differences
between 5 and 6 km is the underestimated backscatter color ratio for the
smoke aerosols. We converted the HSRL backscatter from 532 to 299 nm using a
constant backscatter color ratio, 1.34, which represents an average for the
column-integrated backscatter. The most significant contribution to
integrated backscatter comes from PBL aerosols, which are mostly urban
aerosols with a lower backscatter color ratio than either fresh or aged
smoke (Burton et al., 2012; Cattrall et al., 2005). The uncertainty of the
backscatter color ratio was not considered in the error budget of the
aerosol retrieval. In addition, we ignored the measurement uncertainty of
the HSRL. Therefore, the general agreement of theoretical estimates of
aerosol retrieval uncertainties and the actual errors suggests that our
analysis of the uncertainty sources in Appendix B is reasonable.

We have evaluated the aerosol retrievals at 299 nm from the RO_{3}QET
ozone lidar using both aerosol retrievals at 532 nm from the University of
Wisconsin HSRL and AERONET AOD data at 340 nm from coincident observations
at Huntsville, AL, in 2013. The integrated backscatter coefficients below 6 km a.s.l. from RO_{3}QET and HSRL are highly correlated, with a Pearson
coefficient of 0.99 after excluding cloud-contaminated data. The aerosol
profiles of backscatter coefficients at 30 m vertical and 10 min temporal
resolution retrieved by RO_{3}QET are also highly correlated with those
from the HSRL with a coefficient of 0.95 suggesting that the ozone lidar is
capable of providing reliable aerosol structure information at high
spatiotemporal resolution. Intercomparison of the backscatter product was
performed to avoid additional uncertainty caused by the lidar ratio (*S*)
assumption needed for the HSRL aerosol extinction retrieval. The
RO_{3}QET-measured AOD below 6 km a.s.l. is also highly correlated with the
AERONET-measured AOD, with a correlation coefficient of 0.97. The 340 nm
band of the AERONET AOD data is closest to the ozone lidar wavelength among
the available instruments and can, therefore, provide a constraint for the
*S* assumption for the ozone lidar. Analysis of the intercomparison of AERONET
and RO_{3}QET data confirms that our choice of *S*=60 sr at 299 nm is
appropriate. The aerosol retrieval algorithm and its error budget are shown
in Appendix B. The primary uncertainty sources for the aerosol lidar
retrieval are errors in lidar-signal measurement, boundary value assumption,
air density calculation, *S* a priori value, and ozone profile input. The uncertainty in *S*
assumption is a dominant source at near range, while the lidar-signal
measurement and boundary value errors dominate at far range, as shown in
Fig. B1 for a sample scenario. Within the middle range (PBL top to about 7 km), the air density calculation error is essential and is larger or
comparable to the lidar-signal measurement error. The total uncertainty
generally increases with altitude from about 15 % in the PBL to
consistently higher than 100 % above 7 km. Theoretical estimates of the
error budget are generally consistent with the RO_{3}QET and HSRL measurement
differences.

By assuming a constant *S* of 60 sr at 299 nm, the backscatter coefficients
measured by RO_{3}QET and HSRL are related by a backscatter color ratio
(backscatter-related exponent) of 1.34±0.11 for 299 and 532 nm. The
extinction-related Ångström exponent, which is more relevant for
various applications, is estimated to be 1.49±0.16 by assuming *S*=55 sr for the HSRL at 532 nm. These exponents represent a summertime
average for a mixture of urban pollution and fire smoke. Separation of
aerosol types was not done in this work, although we recognize that *S* and
Ångström exponent vary with the aerosol phase function and size
distribution. Aerosol correction for ozone lidar retrievals will be
described in a subsequent paper.

The ozone DIAL solution can be written as follows:

where *n*_{(r)} is the ozone number density at range *r*; Δ*σ* is the differential ozone absorption cross section;
*P*_{on(r)} and *P*_{off(r)} are the backscattered online
and offline lidar returns; and [*B*] and [*E*] represent the differential
backscatter and extinction terms (Browell et al., 1985), respectively,
including both molecular and aerosol components. The first term of the right-hand
side of Eq. (A1) is often called the signal term. The subscripts “on” and
“off” represent 289 and 299 nm, respectively, in this study. The aerosol extinction
coefficients at 299 nm are calculated using the following procedure.

A first-order Savitzky–Golay differentiation filter with a second-degree polynomial and variable fitting window widths is applied on $\mathrm{ln}\frac{{P}_{\mathrm{on}\left(r\right)}}{{P}_{\mathrm{off}\left(r\right)}}$ to compute the signal term. This smoothing method can accommodate the rapid decay of the lidar signal with altitude to provide sufficient SNR for ozone retrievals by appropriate selection of smoothing window widths (Leblanc et al., 2016).

By canceling the lidar constant using the two lidar equations at ranges *r* and *r*+Δ*r* for 299 nm, the aerosol backscatter coefficients at range *r* can be
expressed as (Uchino et al., 1980)

where *β*_{A}(*r*) and *β*_{M}(*r*) are aerosol and molecular
backscatter coefficients at range *r*, respectively; *Z*(r)=*P*_{off}*r*^{2} is the range-corrected lidar signal at 299
nm; and *α*_{A}(*r*+Δ*r*/2), *α*_{M}(*r*+Δ*r*/2), and
${\mathit{\alpha}}_{{\mathrm{O}}_{\mathrm{3}}}(r+\mathrm{\Delta}r$/2) represent the average aerosol, molecular,
and ozone extinction coefficients, respectively, between ranges *r* and *r*+Δ*r*. Assuming that the 299 nm lidar ratio, *S*=*α*_{A}/*β*_{A}, is constant with the range at 60 sr for this study and further
assuming that

Eq. (A2) contains only two unknown variables: the aerosol backscatter
coefficient *β*_{A}(*r*+Δ*r*) and ozone extinction coefficient
${\mathit{\alpha}}_{{\mathrm{O}}_{\mathrm{3}}}(r+\mathrm{\Delta}r/\mathrm{2}$), which requires knowledge of the ozone
number density ${n}_{(r+\mathrm{\Delta}r/\mathrm{2})}$. Molecular backscatter and extinction
can be computed from nearby radiosonde data or a model with acceptable
accuracy. For the first iteration step, ${n}_{(r+\mathrm{\Delta}r/\mathrm{2})}$ can be
computed from the signal term in Eq. (A1). By assuming a start value
*β*_{A}(ref) at a reference range and a constant *S* with range, *β*_{A}(*r*) can be solved by Eq. (A2). Then, the first *β*_{A}(*r*) profile is substituted back into Eq. (A2) to compute the second
estimate by using a more accurate form for ${\mathit{\alpha}}_{\mathrm{A}}(r+\mathrm{\Delta}r/\mathrm{2}$) as

where ${\mathit{\beta}}_{\mathrm{A}}^{\prime}\left(r\right)$ represents the value from the first
estimate. Typically, a stable solution for *β*_{A}(*r*), which does not
change significantly from one iteration step to the next, can be obtained
with only three iterations of Eqs. (A2) and (A4).

The correction terms, [*B*] and [*E*], in Eq. (A1) are calculated by the Browell
et al. (1985) approximation, assuming a power-law dependence with wavelength
for the aerosol extinction and choosing an appropriate Ångström
exponent. Since this paper focuses only on aerosol retrievals, the details
of the ozone corrections will be described in a future article.

Aerosol profiles computed for the three altitude channels are finally merged into a single profile in their overlapping altitude zones: 0.5–1 km for channels 1 and 2 and 1.5–2 km for channels 2 and 3.

Now we investigate five primary error sources affecting each term on the
right-hand side of Eq. (A2). In the following section, we use the notation
Δ to represent the absolute uncertainty and *δ* to represent
the relative uncertainty. For a function *Y*, derived from several measurement
variables *x*_{1}, *x*_{2}, …, the uncertainty in *Y* can be
estimated by the following expression using the first-order Taylor expansion
approximation when these variables are independent (Taylor, 1997):

## B1 Lidar-signal measurement error

The error source to determine the normalized lidar-signal ratio term
$\frac{Z\left(r\right)}{Z(r+\mathrm{\Delta}r)}\phantom{\rule{0.125em}{0ex}}$ is the lidar-signal measurement error
Δ*P*. Although Δ*P* may be due to various processes such as
inaccurate dead-time correction, inaccurate background subtraction, and
signal-induced noise, its dominant component is the lidar-signal statistical
uncertainty (often called lidar-signal detection noise) and is typically
assumed to obey a Poisson distribution. Assuming no error in deciding *r*, by
using Eqs. (A2) and (B1) we obtain the uncertainty of the aerosol backscatter
owing to lidar-signal measurement error, $\mathrm{\Delta}{\mathit{\beta}}_{\mathrm{A}}^{\mathrm{sig}}\left(r\right)$,
relative to the total backscatter as

where *P*(*r*) represents lidar-signal counts at *r* after omitting the wavelength
subscript (i.e., 299 nm), and *δ**P*(*r*) is just the inverse of SNR. Equation (B2) means that the uncertainty of the aerosol backscatter coefficient due
to lidar-signal measurement is determined by the lidar SNR similarly to
other remote-sensing detection techniques. Consequently, its relative
uncertainty can be written as

where $B\left(r\right)={\mathit{\beta}}_{\mathrm{A}}\left(r\right)/{\mathit{\beta}}_{\mathrm{M}}\left(r\right)$ is the aerosol-to-molecular
backscatter ratio. As expected, $\mathit{\delta}{\mathit{\beta}}_{\mathrm{A}}^{\mathrm{sig}}\left(r\right)$ has a
reverse relationship with *β*_{A}(*r*) since it is a relative
uncertainty. Figure B1 shows an example of the uncertainty budget for a
10 min lidar data profile. The aerosol retrieval uncertainty due to the
lidar-signal measurement error generally increases with altitude primarily
because of the rapidly decaying lidar SNR.

## B2 Boundary value error

According to Eq. (A2), the uncertainty of the aerosol backscatter at *r*,
*β*_{A}(*r*) , can be induced by the uncertainty of the backscatter at
*r*+Δ*r*, *β*_{A}(*r*+Δ*r*), due to the iterative
computation method. The error propagation between the adjacent altitudes can
be determined by their partial differential relationship. Using the
traditional far-end solution by assuming that the air is clean at a
reference altitude, the aerosol uncertainty due to the inaccurate boundary
value assumption propagates downward based on the following equation:

The yellow line in Fig. B1 represents the relative uncertainty of
backscatter retrieval due to the boundary value assumption, $\mathit{\delta}{\mathit{\beta}}_{\mathrm{A}}^{\mathrm{BV}}\left(r\right)$, when *δ**β*_{A}(*r*_{b})=1000 *%* (i.e.,
10 times overestimate at *r*_{b}=10 km). Despite a large overestimate at
the reference altitude, $\mathit{\delta}{\mathit{\beta}}_{\mathrm{A}}^{\mathrm{BV}}\left(r\right)$ decreases toward the
ground to less than 10 % below 5.5 km and less than 1 % below 3.5 km.
Simulations demonstrate that $\mathit{\delta}{\mathit{\beta}}_{\mathrm{A}}^{\mathrm{BV}}\left(r\right)$ for an
underestimation of *δ**β*_{A}(*r*_{b}) (not shown) is
better than that for an overestimation, indicating that the boundary value
is preferred at a smaller value. As suggested by Eq. (B4), $\mathit{\delta}{\mathit{\beta}}_{\mathrm{A}}^{\mathrm{BV}}\left(r\right)$ is affected by both *S* and *B*. Larger *S* (if it is correct) results
in smaller $\mathit{\delta}{\mathit{\beta}}_{\mathrm{A}}^{\mathrm{BV}}\left(r\right)$ and, therefore, aerosol retrieval
errors converge to zero faster. In other words, the smaller the value of *S* is,
the more sensitive the aerosol retrieval is to the boundary value error.
$\mathit{\delta}{\mathit{\beta}}_{\mathrm{A}}^{\mathrm{BV}}\left(r\right)$ decreases with an increase of *B*(*r*). This means
that $\mathit{\delta}{\mathit{\beta}}_{\mathrm{A}}^{\mathrm{BV}}\left(r\right)$ is less affected by the assumed value of
*β*_{A}(*r*_{b}) when the aerosol backscatter becomes more
important relative to molecular backscatter, which occurs at longer
wavelengths or under turbid air conditions. It is to be noted that
*δ**β*_{A}(*r*_{b}) is between −1 and
+∞ so that the distribution of $\mathit{\delta}{\mathit{\beta}}_{\mathrm{A}}^{\mathrm{BV}}\left(r\right)$ is
asymmetric with the zero axis.

In terms of the influence of the boundary value error, we have compared our calculation with an analytical solution proposed by Kovalev and Moosmüller (1994) (not shown); the results are almost identical. Aerosol retrieval uncertainty due to incorrect boundary value assumption tends to converge to zero towards the lidar. It is negligible at lower altitudes, especially in the PBL, when the air is turbid.

## B3 Air density error

According to Eq. (A2), the air density profile affects ${\mathit{\beta}}_{\mathrm{M}}\left(r\right),{\mathit{\beta}}_{\mathrm{M}}(r+\mathrm{\Delta}r)$, and the optical depth (or transmittance). Similarly, we can derive the relative uncertainty in aerosol backscatter owing to the uncertainty in the air density profile as

*S*_{m} represents the molecular extinction-to-backscatter ratio, which is a
constant (8*π*∕3). The two parts in the square root are the components
due to the uncertainties at *r* and *r*+Δ*r*. Each component
includes the influences from both molecular backscatter and optical depth.
When Δ*r* is small, the contribution of the optical depth error is much
smaller than that of the molecular backscatter error, so Eq. (B4) can be
approximated as

It is to be noted that Δ*β*_{M}(*r*) and Δ*β*_{M}(*r*+Δ*r*) are independent errors as assumed in Eq. (B1). If they
are correlated, Eq. (B5) will partly cancel out with their covariance term,
which is not shown in Eq. (B1). Due to the nature of the iterative computation
method, $\mathit{\delta}{\mathit{\beta}}_{\mathrm{A}}^{\mathrm{AD}}(r+\mathrm{\Delta}r)$ affects $\mathit{\delta}{\mathit{\beta}}_{\mathrm{A}}^{\mathrm{AD}}\left(r\right)$ as noted in Eq. (B4), so the aerosol retrieval
uncertainty due to air density error will propagate downward. However, model
simulation suggests that the systematic error of the air density calculation
has little impact on the aerosol retrieval because of the cancelation of the
effect at *r* and *r*+Δ*r*. Equation (B6) means the uncertainty in the
calculation of molecular backscatter will mostly
linearly propagate to
aerosol backscatter. If the 2*σ* precisions of a radiosonde are 0.3 K
and 0.5 hPa for temperature and pressure measurements (Hurst et al., 2011),
the propagated uncertainty onto molecular backscatter is only about 0.1 %.
However, the real disturbance of an atmosphere deviating from the actual air
density profile may be more significant since there are usually only a few
radiosonde profiles available every day. Hence, we assume *δ**β*_{M}(*r*) to be 1 %, and the resulting aerosol retrieval uncertainty is
represented by the green line in Fig. B1. $\mathit{\delta}{\mathit{\beta}}_{\mathrm{A}}^{\mathrm{AD}}\left(r\right)$
can be tens of percent in the free troposphere and is an important error
source for aerosol retrievals (Russell et al., 1979). $\mathit{\delta}{\mathit{\beta}}_{\mathrm{A}}^{\mathrm{AD}}\left(r\right)$ is less than 10 % in the PBL because of more turbid air
in that region. Since *δ**β*_{M}(*r*) is assumed to be a constant
in this example, the variation of $\mathit{\delta}{\mathit{\beta}}_{\mathrm{A}}^{\mathrm{AD}}\left(r\right)$ is mostly
a result of varying *B*(*r*), which is the aerosol-to-molecular backscatter ratio. Since
*B*(*r*) generally increases with an increase in wavelength, $\mathit{\delta}{\mathit{\beta}}_{\mathrm{A}}^{\mathrm{AD}}\left(r\right)$ is expected to be smaller at longer wavelengths.
Therefore, the aerosol retrieval is less sensitive to the air density error
at longer wavelengths.

## B4 Lidar ratio error

By using Eqs. (A2) and (B1), the relative uncertainty in aerosol backscatter
due to incorrect lidar ratio (*S*) assumption can be calculated as follows:

$\mathit{\delta}{\mathit{\beta}}_{\mathrm{A}}^{S}\left(r\right)$ due to Δ*S* at only range *r* appears to be
small, about 1 %, when Δ*r* is specified at 22.5 m. However, Δ*S* varying with altitude is mostly systematic; therefore, $\mathit{\delta}{\mathit{\beta}}_{\mathrm{A}}^{S}\left(r\right)$ at every altitude will propagate downward, and these
effects will accumulate. The error accumulation is not straightforward to
compute as an analytical solution. However, these effects can be simulated
numerically. *S* is highly variable, and it is difficult to estimate its actual
uncertainty range. In this study, we assume that *δ**S*=20 % (or
Δ*S*=12 sr) according to both a previous study (Müller et al.,
2007) and the analysis using the colocated AERONET AOD data at 340 nm. The
light blue line in Fig. B1 shows that the accumulative uncertainties in
the aerosol backscatter due to Δ*S* using Eqs. (B7) and (B4) are close
to the assumed 20 % uncertainty for *δ**S*; $\mathit{\delta}{\mathit{\beta}}_{\mathrm{A}}^{S}\left(r\right)$ is the largest error source in the PBL, which is the near range of the
lidar measurement. $\mathit{\delta}{\mathit{\beta}}_{\mathrm{A}}^{S}\left(r\right)$ decreases with an
increase in wavelength because of increasing *B*(*r*). In other words, $\mathit{\delta}{\mathit{\beta}}_{\mathrm{A}}^{S}\left(r\right)$ is less sensitive to Δ*S* at longer
wavelengths.

## B5 Ozone error

Similar to *S*, the ozone uncertainty affects only the transmittance term in
Eq. (A2), and its error propagation on aerosol backscatter retrieval can be
expressed as

$\mathit{\delta}{\mathit{\beta}}_{\mathrm{A}}^{{\mathrm{O}}_{\mathrm{3}}}\left(r\right)$ is proportional to the $\left[\frac{\mathrm{1}}{B\left(r\right)}+\mathrm{1}\right]$ factor and ozone absorption
uncertainty, meaning that $\mathit{\delta}{\mathit{\beta}}_{\mathrm{A}}^{\mathrm{O}\mathrm{3}}\left(r\right)$ is smaller at
longer wavelengths due to larger aerosol scattering ratio and smaller ozone
absorption. When Δ*r* is specified at 22.5 m, $\mathit{\delta}{\mathit{\beta}}_{\mathrm{A}}^{\mathrm{O}\mathrm{3}}\left(r\right)$ is less than 0.3 %. We still simulate the vertical accumulation of
$\mathit{\delta}{\mathit{\beta}}_{\mathrm{A}}^{\mathrm{O}\mathrm{3}}\left(r\right)$ using Eq. (B4). As noted earlier, the
systematic errors of the DIAL ozone measurement tend to accumulate, while the
random errors tend to cancel out. The dominant error source for lidar
measurements at the far range is typically the lidar-signal detection noise,
a type of random error. Therefore, for purposes of estimation, we assume a
5 % constant DIAL retrieval uncertainty primarily covering the
uncertainties due to ozone absorption cross section, non-ozone gas
interference, and signal saturation effect (Leblanc et al., 2018; Wang et
al., 2017). As shown in Fig. B1, the simulated aerosol retrieval
uncertainty due to ozone is relatively minor and is less than 5 % at most
altitudes.

In summary, the uncertainties in aerosol backscatter retrieval for the ozone
lidar are controlled by Δ*S* at near ranges (i.e., in the PBL) where
the air is most turbid and are determined by both the lidar-signal detection
error and inaccurate boundary value assumption at far ranges (higher than 7 km) where the air is typically clear. In the middle range of the lidar
measurement (PBL top to 7 km), the air density calculation error may become
a significant error source for aerosol retrieval and may have a comparable
influence on the aerosol retrieval as the lidar-signal measurement error.
Relative to the four above uncertainty sources, ozone DIAL retrieval error
is relatively unimportant, especially in the lower altitudes where lidar SNR
is large enough. All the uncertainty terms are affected by the
aerosol-to-molecular backscatter ratio, *B*(*r*), which represents the relative
importance of the aerosol component in both extinction and backscatter
processes. Based on the above uncertainty budget analysis, we conclude that
the RO_{3}QET lidar is capable of measuring aerosol profile reliably below
6 km with the current laser output power.

The ozone lidar data are available at https://doi.org/10.5067/LIDAR/OZONE/TOLNET (TOLNet Science Team, 2020).

The HSRL data used in this study can be obtained at the University of Wisconsin lidar website: http://hsrl.ssec.wisc.edu/ (last access: 20 September 2020, Eloranta et al., 2020).

SK designed the evaluation experiments, developed the aerosol retrieval algorithm, and prepared the original manuscript. BW carried out the experiments and performed the analysis of all datasets. MJN was responsible for funding acquisition. KK provided the AERONET aerosol data used in this study. EWE, JPG, and IR made the HSRL observations and provided the HSRL dataset. CJS, TAB, and GG contributed to the analysis of aerosol retrieval uncertainty. All listed authors contributed to the review and editing of this paper.

The authors declare that they have no conflict of interest.

The authors thank the Tropospheric Composition Program of the National Aeronautics and Space Administration (NASA) Science Mission Directorate for supporting the TOLNet program. The views, opinions, and findings contained in this report are those of the authors and should not be construed as an official NASA; National Oceanic and Atmospheric Administration; or US Government position, policy, or decision.

This research has been supported by the National Aeronautics and Space Administration (grant nos. 80NSSC19K0247, 80NSSC19K0248, and 80NM0018D0004).

This paper was edited by Piet Stammes and reviewed by two anonymous referees.

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- Abstract
- Introduction
- Instruments and data processing
- Intercomparison results
- Conclusions
- Appendix A: Aerosol retrieval algorithm
- Appendix B: Error budget of the aerosol retrieval
- Data availability
- Author contributions
- Competing interests
- Acknowledgements
- Financial support
- Review statement
- References

- Abstract
- Introduction
- Instruments and data processing
- Intercomparison results
- Conclusions
- Appendix A: Aerosol retrieval algorithm
- Appendix B: Error budget of the aerosol retrieval
- Data availability
- Author contributions
- Competing interests
- Acknowledgements
- Financial support
- Review statement
- References